 Stress has units: N/m 2 or lb f /in 2 Engineering Stress Shear stress,  : Area, A F t F t F s F F F s  = F s A o Tensile stress,  : original area before loading Area, A F t F t  = F t A o 2 f 2 m N or in lb =

Simple tension: cable Note:  = M/A c R here. Common States of Stress A o = cross sectional area (when unloaded) FF o   F A o   F s A  M M A o 2R2R F s A c Torsion (a form of shear): drive shaft

(photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o   F A Simple compression: Note: compressive structure member (  < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES A o Balanced Rock, Arches National Park

Bi-axial tension: Hydrostatic compression: Pressurized tank   < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES Fish under water  z > 0  

Tensile strain: Lateral strain: Shear strain: Strain is always dimensionless. Engineering Strain  90º 90º -  y xx   =  x/y = tan   L  L w o  /2  L L o w o

Linear Elastic Properties Hooke's Law:  = E   Linear- elastic E  F F simple tension test (If there is a linear response)

Modulus of Elasticity Modulus of Elasticity, E: (also known as Young's modulus) “Stiffness” of the material Linear behavior typically seen in metals and ceramics Other materials do not have linear response (Grey cast iron, concrete, most polymers) Tangent modulus: slope of stress strain curve at some specified level of stress Units: Pressure (psi) Secant modulus: slope of a secant drawn form the origin to some point on the stress strain curve

Atomic Behavior Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

Effect of Temperature E = f (T)